On 5-Uniform Delta-Systems with 3 Edges

The complete 5-uniform hypergraph of order v has a set V of size v as its vertex set and the set of all 5-element subsets of V as its edge set. A delta-system with 3 edges in such a hypergraph has edge set {e1, e2, e3} such that ei 8́♭ ej = W for every i =Ìı j, where 8́ĐW8́Đ is 0, 1, 2, 3, or 4. We give necessary and sufficient conditions for the existence of a decomposition of the complete 5-uniform hypergraph of order v into isomorphic copies of all possible delta-systems with 3-edges.